The ionic environment determines ribozyme cleavage rate by modulation of nucleobase pK _a

Abstract

Several small ribozymes employ general acid–base catalysis as a mechanism to enhance site-specific RNA cleavage, even though the functional groups on the ribonucleoside building blocks of RNA have pK _a values far removed from physiological pH. The rate of the cleavage reaction is strongly affected by the identity of the metal cation present in the reaction solution; however, the mechanism(s) by which different cations contribute to rate enhancement has not been determined. Using the Neurospora VS ribozyme, we provide evidence that different cations confer particular shifts in the apparent pK _a values of the catalytic nucleobases, which in turn determines the fraction of RNA in the protonation state competent for general acid–base catalysis at a given pH, which determines the observed rate of the cleavage reaction. Despite large differences in observed rates of cleavage in different cations, mathematical models of general acid–base catalysis indicate that k ₁, the intrinsic rate of the bond-breaking step, is essentially constant irrespective of the identity of the cation(s) in the reaction solution. Thus, in contrast to models that invoke unique roles for metal ions in ribozyme chemical mechanisms, we find that most, and possibly all, of the ion-specific rate enhancement in the VS ribozyme can be explained solely by the effect of the ions on nucleobase pK _a. The inference that k ₁ is essentially constant suggests a resolution of the problem of kinetic ambiguity in favor of a model in which the lower pK _a is that of the general acid and the higher pK _a is that of the general base.

INTRODUCTION

The small nucleolytic ribozymes (hammerhead, hairpin, HDV, VS, and GlmS) all perform site-specific RNA self-cleavage, yielding products with 2′,3′ cyclic phosphate and 5′ hydroxyl termini. These products imply a common reaction pathway in which the 2′ hydroxyl attacks the adjacent phosphorous and the downstream 5′ oxygen departs, thereby breaking the backbone; however, the mechanism(s) by which these ribozyme catalyze cleavage is still incompletely understood (Lilley and Eckstein 2008).

The observed rate of RNA cleavage by a given ribozyme can differ by several orders of magnitude depending on which cation is present in the reaction solution (Murray et al. 1998; Curtis and Bartel 2001; O'Rear et al. 2001; Perrotta and Been 2006; Poon et al. 2006; Roychowdhury-Saha and Burke 2006). Typically, the observed rate of a cleavage reaction is much faster in divalent than in monovalent ions. Hypothetically, this might be due to a direct increase in the rate of the bond-breaking step if, for example, the divalent ion were specifically positioned to neutralize the developing negative charge on the phosphate during the transition state or interact with the 2′ or 5′ oxygens, as has been found for other ribozymes, such as Group I and II introns (Shan et al. 1999; Zhang and Doudna 2002; Stahley and Strobel 2005; Gordon et al. 2007). Alternatively, the divalent ion may play an indirect role, such as in positioning of the catalytic functional groups, in a variety of electrostatic effects in the transition state and/or ground state, or in modulating the pK _a of a functional group involved in general acid or general base catalysis (Fedor 2002; Emilsson et al. 2003; Kraut et al. 2003; Lonnberg and Lonnberg 2005; Hoogstraten and Sumita 2007; Scott 2007; Sigel and Pyle 2007). The mechanism(s) by which cations contribute to rate enhancement continues to be a matter of considerable discussion (Fedor 2002; Perrotta and Been 2006; Sigel and Pyle 2007).

In RNA cleavage via general acid–base catalysis, an unprotonated functional group, the general base, removes a proton from the 2′-OH and a protonated functional group, the general acid, donates a proton to the 5′ oxygen leaving group. In protein ribonucleases, such as RNaseA, histidine residues function well in general acid–base catalysis because the imidazole side chain of histidine has a pK _a near neutral pH that can readily accept or donate a proton under physiological conditions (Raines 1998). In contrast, the ribonucleoside building blocks of RNA have pK _a values around pH 4 for adenosine and cytosine and above pH 9 for guanosine and uridine (Clauwaert and Stockx 1968), superficially making it unlikely that ribozymes could use general acid–base catalysis effectively in the biological environment. Nonetheless, experimental evidence supports a role for general acid–base catalysis in all of the small ribozymes (Nakano et al. 2000; Pinard et al. 2001; Shih and Been 2001; Das and Piccirilli 2005; Han and Burke 2005; McCarthy et al. 2005; Wilson et al. 2006, 2007; Cochrane et al. 2007; Klein et al. 2007; Smith and Collins 2007; Bevilacqua 2008). In some cases, the apparent pK _a values of unpaired or non-Watson–Crick paired bases are shifted substantially toward neutrality by the local environment, for example, by base stacking, hydrogen bonding, and proximity to the strong negative charge of backbone phosphates or the strong positive charge of bound divalent cations (Luptak et al. 2001; Fedor 2002; Sigel 2004; Gong et al. 2007).

In this paper, we present evidence that most, if not all, of the ion-dependent rate enhancement observed in cleavage by the VS ribozyme can be accounted for by the effect of the ions on nucleobase pK _a and not to direct participation of the metal ion in the chemical step of the reaction. The relationships among the ionic environment, catalytic pK _a values, and the observed reaction rate may also apply to other catalysts that employ similar mechanisms, including other nucleolytic ribozymes and possibly protein enzymes.

RESULTS AND DISCUSSION

In the simplest model of general acid–base catalysis, the experimentally observed rate of cleavage, k _obs, is related to the intrinsic rate of the bond-breaking step, k ₁, by

where F represents the fraction of RNA in the catalytically competent state. k ₁ is a function of the Brønsted α and β values of the general acid and base, respectively, and is not affected by pH. F is the proportion of the RNA capable of participating in catalysis: in the simplest model, this is the proportion of RNA in which the general acid and general base are in their protonated and deprotonated states, ,and respectively. and are functions of pH and depend on the pK _a values of the general acid and base and the pH at which the reaction is performed (Bevilacqua 2003; Jaikaran et al. 2008). We have recently incorporated an additional term into F that describes the cooperative loss of activity at very low pH; this term is a function of pH and the number of sites that contribute to the inactivation of the ribozyme when protonated (Bevilacqua 2003; Jaikaran et al. 2008; see Materials and Methods).

We have previously found that the fast cis-cleaving RG version of the VS ribozyme exhibits a bell-shaped k _obs versus pH curve with apparent pK _a values of 5.8 and 8.3 in saturating concentrations of Mg²⁺ (Fig. 1A; Table 1; Smith and Collins 2007). Similar observations have been made with a trans-cleaving version of the ribozyme (Wilson et al. 2007). A kinetic solvent isotope effect has been observed for the RG ribozyme, indicative of a rate-limiting proton transfer step in a general acid–base catalyzed reaction (Smith and Collins 2007).

FIGURE 1.

Cleavage rate versus pH curves for the VS ribozyme in different ionic environments. The apparent first-order cleavage rate constant, k _obs, of the RG version of the VS ribozyme was determined in the presence of the indicated cations over the pH range indicated (open symbols): (A) 200 mM MgCl₂; (B) 2.5 M LiCl + 20 mM MgCl₂; (C) 2.5 M LiCl; (D) 2.5 M NaCl. Control experiments showed that the concentrations of cations used were saturating across the pH range examined (see Materials and Methods). Data were fit to either of two kinetically ambiguous models of general acid–base catalysis that also included a term describing the cooperative loss of activity at low pH (Jaikaran et al. 2008) (solid lines; see Materials and Methods). In Model 1, the lower pK _a is assigned to the general base and the higher pK_a to the general acid; these assignments are reversed in Model 2. Dotted and dashed lines describe the titration of the general acid (), and the general base plus the contribution from cooperative loss of activity below pH 4 respectively, having the pK _a values inferred from the data. The intrinsic rate of the bond-breaking step, k ₁, is indicated by the arrows. Parameter values are presented in Table 1.

TABLE 1.

Estimation of cleavage rate constants and pK _a values in different ionic environments^a

In the VS ribozyme, nucleobases A756 and G638 have been implicated as the most likely candidates for the catalytic nucleobases (Andersen and Collins 2000; Hiley et al. 2002; Jones and Strobel 2003; Smith and Collins 2007; Wilson et al. 2007; Jaikaran et al. 2008). Determining which nucleobase functions as the general acid and which as the general base is challenging for any enzyme because a k _obs versus pH curve obtained under a single set of experimental conditions can be equally explained by either of two kinetic models (Fig. 1; for the principle of kinetic ambiguity, see Jencks 1969; see Materials and Methods). In Model 1, the lower pK _a represents the general base and the higher pK _a represents the general acid; in Model 2, these assignments are reversed. Importantly for the analysis below, the models also differ substantially in their estimate of k ₁ (Fig. 1). Analyzing k _obs versus pH curves for the RG ribozyme in different ionic environments provided evidence that Model 2 provides the more parsimonious explanation of the overall data (see below), implying that the nucleobase with the lower pK _a, possibly A756, is the general acid and the nucleobase with the higher pK _a, possibly G638, is the general base.

The pH–rate profile for RG cleavage in saturating concentrations of Li⁺ is bell-shaped between pH 4.5 and 9 (Fig. 1C). The plateau of the curve is flatter and broader in Li⁺ than in Mg²⁺, with apparent pK _a values of 4.9 and 8.8, and the maximum k _obs is about 50-fold slower than in Mg²⁺ (Table 1). Repeating the Li⁺ pH–rate experiments in D₂O instead of H₂O showed a kinetic solvent isotope effect, indicating that the reaction in Li⁺ is rate-limited by proton transfer, consistent with general acid–base catalysis, as in Mg²⁺ (Fig. 2A; Smith and Collins 2007).

FIGURE 2.

Cleavage of RG in Li⁺ or Na⁺ but not K⁺ exhibits a kinetic solvent isotope consistent with rate-limiting proton transfer in a general acid–base catalyzed reaction. Cleavage reactions were performed and analyzed as described in Materials and Methods using (A) 2.5 M LiCl, (B) 2.5 M NaCl, or (C) 2.5 M KCl. “pL” refers to pH (for reactions in H₂O; closed symbols) or pD (for reactions in D₂O; open symbols).

It would be tempting to conclude that self-cleavage is faster in Mg²⁺ than in Li⁺ because Mg²⁺ performs an additional role in catalysis that contributes a 50-fold enhancement to k ₁, the instrinsic rate of chemistry. For example, it is easy to imagine that the stronger electronegativity or the particular coordination geometry of Mg²⁺ might allow it to contribute more effectively to nucleobase positioning, or electrostatic catalysis than Li⁺, thereby making catalysis intrinsically faster in Mg²⁺. Fitting the k _obs versus pH data to Model 1 could accommodate this interpretation because k ₁ effectively becomes a variable that is free to acquire different values in different reaction conditions, as needed to fit the observed data (Table 1). However, when we fit the data using Model 2, we noticed that the differences in pK _a values in Mg²⁺ versus Li⁺ produced estimates of k ₁ that were within twofold of each other (9 × 10⁴ min⁻¹ versus 5 × 10⁴ min⁻¹) despite the 50-fold difference in k _obs (Table 1). The slightly higher estimate of k ₁ in Mg²⁺ may represent a small Mg²⁺-specific rate enhancement, or it may be the result of cumulative errors of the parameters used to make the estimate. Putting this another way, if we assume that k ₁ is truly constant for a given ribozyme, the differences in apparent pK _a values of the ribozyme in Mg²⁺ versus Li⁺ are enough to explain almost all of the 50-fold difference between the observed cleavage rates.

To further test the correlation between k _obs and pK _a, we measured the cleavage rate versus pH for the same ribozyme in the presence of other cations. The observed rate in Na⁺ is more than 3000-fold slower than in Mg²⁺, and we find that the apparent pK _a values are even further apart (Fig. 1D, <4.5 and >9), in fact, sufficiently far from neutral pH that additional effects observed at extreme pH prevent their accurate measurement (Jaikaran et al. 2008; see Materials and Methods). Kinetic solvent isotope experiments confirmed that the reaction in Na⁺ was limited by proton transfer, as in Mg²⁺ and Li⁺ (Fig. 2B). If we assume that the lower apparent pK _a in Na⁺ has a value typical of an adenosine in a single-stranded RNA (pK _a ≈ 3.7) (Moody et al. 2005) and the upper pK _a has a value typical of guanosine (pK _a ≈ 9.3) (Da Costa and Sigel 2003), then the estimate from Model 2 is k ₁ ≈ 4 × 10⁴ min⁻¹, almost the same as in Li⁺ and about twofold lower than in Mg²⁺ (Table 1). Considering the 3000-fold range in k _obs among reactions in Mg²⁺, Li⁺, and Na⁺, the small differences in the estimates of k ₁ among these ionic conditions are consistent with the idea that the value of k ₁ is essentially the same in each ionic condition.

Cleavage in the presence of only K⁺ is rate limited by a step that does not involve proton transfer and is thus not relevant to the current analysis (Fig. 2C). The concentration of Ca²⁺ required for saturation varied substantially with pH (see Materials and Methods), complicating analysis of pH–rate data. We were able to measure single pK _a values in NH₄ ⁺ or Mn²⁺ (Fig. 3; Table 1); however, chemical properties of the individual cations prevented detection of putative pK _a values above pH 8 (see Materials and Methods). Therefore, to further test the correlation between ribozyme pK _a and k _obs, we measured pK _a values in a combination of cations that gave maximal k _obs values between those of the individual ions (Fig. 1B). The maximal k _obs in 2.5 M Li⁺ plus 20 mM Mg²⁺ is approximately fivefold faster than in Li⁺ alone, and the apparent pK _a values are shifted a combined ∼0.5 pH unit closer together, leading to an estimate of k ₁ = 5 × 10⁴ min⁻¹, similar to the estimates in all of the other ionic conditions examined (Table 1).

FIGURE 3.

Rate versus pH curves for RG in NH₄ ⁺ or Mn²⁺. The apparent first-order cleavage rate constant, k _obs, of the RG version of the VS ribozyme was determined in the presence of (A) 3.75 M NH₄Cl and (B) 25 mM MnCl₂. Data in NH₄Cl were fit to Equation 3 and data in MnCl₂ were fit to Equation 4 (solid lines), as described in Materials and Methods. Parameter values are presented in Table 1.

The theoretical relationship between k _obs of a ribozyme reaction employing general acid–base catalysis and the magnitude of the difference between the pK _a of the general acid and base (ΔpK _a = | pK _aA – pK _aB |) has been described previously (Fig. 4A, solid line; Bevilacqua 2003): For every pH unit that these pK _a values move farther apart, k _obs decreases by a factor of 10, thus a plot of log₁₀ k _obs versus ΔpK _a would have a slope of −1 if k _obs were completely determined by general acid–base catalysis. The observed data fit this relationship quite well (Fig. 4A, open symbols). Because k ₁ is a true constant in Model 2 but a variable in Model 1, Model 2 provides a more parsimonious explanation of the relationship between k _obs and ΔpK _a. Alternative roles of individual types of ions are not consistent with this relationship. For example, if each type of ion made unique electrostatic or other contributions to the observed rate of cleavage without affecting nucleobase pK _a, the data points in Figure 4A would fall on a vertical line with an x-axis value equal to the intrinsic ΔpK _a of the catalytic nucleobases; if each type of ion indeed altered the pK _a of the catalytic nucleobases, but such alterations did not cause the observed change in the rate of cleavage, the k _obs versus ΔpK _a data points would be scattered on this graph. The observed relationship suggests that the rate of cleavage of the RG ribozyme in a given ionic environment is largely determined by the difference between the apparent pK _a values of the general acid and general base.

FIGURE 4.

Ionic environment determines the apparent pK _a of the general acid and general base and the observed rate of cleavage. (A) The logarithm of the maximal observed rate of cleavage in a given ionic condition, log₁₀k_obs^max, is plotted as a function of the absolute value of the difference between pK_aA and pK_aB (| ΔpK_a |). The solid line describes the theoretical relationship between ΔpK_a and log₁₀k_obs^max for a reaction catalyzed solely by general acid–base catalysis with k₁ = 5.8 × 10⁴ min⁻¹ (the mean of the estimates of k₁ in the four ionic conditions examined in Fig. 1; see Table 1). Dotted gridlines are included to emphasize the linear relationship between the y- and x-axis variables over most of the pH range. (B) log₁₀k_obs^max is plotted as a function of the values of pK _aA (open symbols) or pK _aB (filled symbols) in Mg²⁺ (○); Mn²⁺ (▽); Mg²⁺+Li⁺ (△); Li⁺ (□) NH₄⁺ (∗); and Na⁺ (⋄). Symbols for NH₄ ⁺ and Na⁺ lie on top of each other in B. Error bars indicate the upper and lower range of pK _a estimates including uncertainties from all sources (see Materials and Methods); error bars in A are the sum of the error bars in B. pK _aB could not be experimentally determined for some cations due to oxidation of the metal ion, RNA degradation, or buffering by the metal ion at high pH (see Materials and Methods).

Three situations could produce the results described in Figure 4A: the pK _a of the general base could be unchanged in the different ionic conditions, and the pK _a of the general acid could be altered, or vice versa, or the pK _a values of both could change. Plotting the maximal observed cleavage rate in each ionic condition as a function of the individual apparent pK _a values of the general acid or general base in each ionic condition produced striking log–linear relationships in both cases (Fig. 4B). Cleavage rates in Mn²⁺ or NH₄ ⁺, for which only the lower pK _a could be estimated (Fig. 3), also fell on the same line (Fig. 4B). Thus, the observed differences in ΔpK _a in different ionic environments are the result of both pK _a values being shifted toward neutrality by specific amounts characteristic of each type of cation.

There are a number of mechanisms by which metal ions could function as modulators of the pK _a of a nucleobase (for a recent review, see Sigel and Pyle 2007). The most direct would be that the metal ion binds to the nucleobase and stabilizes or destabilizes a particular protonation state. Indirect effects, in which the metal ion binds via a water molecule or even to another nearby nucleobase and alters the electrostatic environment of the catalytic nucleobase, could also account for our observations. The relationships described in Figure 4 among cation identity, pK _a of the catalytic nucleobases, and observed catalytic rate might apply to other ribozymes and maybe even to proteins or other catalysts that utilize general acid–base catalysis. Shifted pK _a values are observed in the active sites of several protein enzymes (for review, see Harris et al. 2002). Examples in which metal ion identity affects the apparent pK _a of protein-catalyzed reactions include the nucleotidyl transfer by a viral RNA polymerase and GTP hydrolysis by p21^ras (Schweins et al. 1997; Bowers et al. 2007; Castro et al. 2007). Further testing of these relationships should be possible using enzymes in which (1) the cation does not play an obligatory role in the catalytic mechanism; (2) general acid–base catalysis is the rate-limiting step across the pH range examined; and (3) both pK _a values can be experimentally measured.

In summary, we provide evidence that the intrinsic rate of the bond-breaking step, k ₁, is constant irrespective of the identity of the cation(s) in the reaction solution for a ribozyme that employs general acid–base catalysis. We propose that the differences in experimentally observed cleavage rates in different ions are the result of the ionic environment endowing the nucleobases that participate in general acid–base catalysis with particular pK _a values. This in turn determines the fraction of the RNA in the catalytically competent protonation state at a given pH, which determines the experimentally observed cleavage rate.

MATERIALS AND METHODS

RNA synthesis and cleavage reactions

RNAs were synthesized by in vitro transcription and purified as described (Hiley and Collins 2001). Cleavage reactions were initiated by mixing 1 volume of 1× reaction mix (50 mM buffer, 2 mM spermidine, 50 mM KCl) containing 2× RNA with 1 volume of 1× reaction mix containing 2× cation to obtain final concentrations of RNA=5–10 nM and cation as indicated in Figures 1–3 and 5. Reactions with rate constants >6 min⁻¹ were performed using a Kintek RQF-3 instrument (Kintek Corp.). Buffers, pH measurements, and data quantification were done as previously described (Jaikaran et al. 2008). Estimates of k _obs in a given reaction condition typically varied by less than ±20% in replicate experiments.

FIGURE 5.

Determining the concentration of cation required to obtain maximal cleavage rate over the pH range examined. Cleavage rate constants were determined in 1× reaction solutions at the indicated pH containing the indicated concentrations of (A) MgCl₂, (B) LiCl, (C) NaCl, (D) NH₄Cl, (E) CaCl₂, and (F) MnCl₂. Data are plotted as a fraction of maximal k _obs at the indicated pH. Data in B were fit to the Hill equation (solid lines); other lines simply connect the data points. The dashed line in B illustrates inhibition, by an unknown mechanism, at LiCl concentrations above 2.5 M at pH 9.1. High concentrations of Ca²⁺ at high pH also inhibit ribozyme cleavage by an unknown mechanism.

As will be reported in detail elsewhere (M.D. Smith and R.A. Collins, unpubl.) we observed effects of high salt concentrations on the measured pH of the reaction solutions. Others have also reported effects of high ionic strength on the real solution pH and/or the pH electrode used for measurement (Perrotta and Been 2006; Salis et al. 2006). Extensive control experiments provided evidence that the pH values that we report in Figures 1–3 and 5 are not confounded by errors due to ionic effects on pH measurement but are indeed the pH values (±0.1 pH unit) of the 1× reaction solutions at 37°C. pH–rate profiles in Figures 1–3 were collected using a concentration of metal ion that was saturating for ribozyme activity across the entire pH range (as determined in Fig. 5). Because metal ions altered the pH of the 1× reaction solutions, the pH of the 1× reaction solutions containing different concentrations of cations were adjusted to be within <0.1 pH unit of the pH indicated in Figure 5. This ensured that changes in cleavage rate were due solely to differences in metal ion concentrations and not to an effect of metal ions on the pH of the solution. Data were not collected above pH 7.5 in NH₄Cl because high concentrations of NH₄ ⁺ strongly buffer above pH 7.5. Data in MnCl₂ could not be collected above the pH 8.0 due to oxidation of Mn²⁺.

Data analysis

Rate constants and pK _a values were determined from the following relationships, as described elsewhere (Bevilacqua 2003; Jaikaran et al. 2008):

where k _obs is the experimentally estimated apparent rate constant, F is the fraction of RNA in the catalytically competent state at a given pH, and k ₁ is the intrinsic rate constant of the bond-breaking step, which is unaffected by pH.

F is the product of several proportions, including: (1) , and which describe the proportion of the RNA in which the general acid and general base (having pK _aA and pK _aB) are in their protonated and deprotonated states, respectively; and (2) f _C, which represents the fraction of RNA retaining critical tertiary interactions, described by an additional pK _a (pK _aC) and a cooperativity coefficient (n). Thus, F can be described by

Simulations showing the effect of pH on F (Equation 2) for Models 1 and 2 are presented in Figure 6. By substituting Equation 2 into Equation 1, experimental k _obs versus pH data were fit using nonlinear least-squares minimization to allow simultaneous estimation of optimal values for k ₁, pK _aA, pK _aB, pK _aC, and n in each ionic environment examined (Jaikaran et al. 2008). Due to the inability to collect data at high pH, data collected in NH₄Cl or MnCl₂ were fit with Equation 3 or 4, respectively:

FIGURE 6.

Simulations showing the effect of pH on the proportion of RNA in the state capable of participating in catalysis for Models 1 and 2 (see Materials and Methods). The figure shows individual plots of log₁₀ of the fraction of RNA (F) in which the general acid (, short dashed line) or general base (, long dashed line) are in the appropriate protonation state to participate in catalysis as a function of pH; in Model 1, the general base pK _aB = 6 and the general acid pK _aA = 8; in Model 2, the general base pK _aB = 8 and the general acid pK _aA = 6. A third plot (solid black line) describes the fraction of RNA that retains critical tertiary interactions (f _C) that are disrupted below an apparent pK _aC = 4 and n = 5 (see Materials and Methods). Multiplying the three proportions describes F, the overall fraction of RNA in the catalytically competent state at a given pH (○).

Multiple cycles of enforcing different values on pK _a estimates and re-estimating the remaining parameters suggested that our estimates for pK _a values of bell-shaped curves are within ±0.1 pH unit. As discussed by Jaikaran et al. (2008), pK _a values that are low enough to be in the region of the curve affected by the cooperative loss of activity at low pH (described by pK _aC and n) cannot be estimated accurately. This is the situation for reactions in NaCl or NH₄Cl. In these cases, we have estimated pK _aA as that of an unshifted adenosine in a single-stranded RNA (Moody et al. 2005). The error bars for these ions in Fig. 4B represent the range of values that pK _aA may have, which would otherwise be obscured by the cooperative loss of activity.